Develop a program that takes a binary as input and determines the longest dependency chain/dataflow path through the binary. Assuming every instruction has a delay of 1 cycle before it can forward its output (via registers or memory) to subsequent instructions, how many cycles does it take to execute every instruction in a binary? You don't have to model any real architectural bottlenecks, and can assume perfect caching and branch prediction.

The loop body has several operations that depend on the subtract from the previous iteration:

The N(number of iterations) subtracts cyclically feed one another, creating a dependency chain of N steps

The last subtract has a dependency chain of two - the compare and not-taken conditional jump

The second to last subtract has a dependency chain of three - the move→add→move chain

The last two moves - outside the loop - can be issued early, and are thus off the critical path.

The final syscall (int $0×80) is dependent on all instructions, and thus the loop dataflow.

This means the dataflow depth is 2 + N-1(subtracts) + 3(mov→add→mov) + 1(syscall) = 2 + 13 + 3 + 1 = 19. This is the number your program should print for this loop program as input.
You could also get this as 2 + N(subtracts) + 2(cmp→branch) + 1(syscall) since the sub(N-1)→mov→add→move is in parallel with sub(N-1)→sub(N)→cmp→jmp.